Open AccessOptimal control of stochastic system with Fractional Brownian Motion
Author(s) -
Chaofeng Zhao,
Zhibo Zhai,
Qinghui Du
Publication year - 2021
Publication title -
mathematical biosciences and engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.451
H-Index - 45
eISSN - 1551-0018
pISSN - 1547-1063
DOI - 10.3934/mbe.2021284
Subject(s) - fractional brownian motion , martingale (probability theory) , mathematics , brownian motion , population , mathematical optimization , markov process , stochastic control , markov chain , geometric brownian motion , stochastic process , optimal control , stochastic modelling , computer science , diffusion process , statistics , knowledge management , demography , innovation diffusion , sociology
In this paper, we introduce a class of stochastic harvesting population system with Fractional Brownian Motion (FBM), which is still unclear when the stochastic noise has the character of memorability. Stochastic optimal control problems with FBM can not be studied using classical methods, because FBM is neither a Markov pocess nor a semi-martingale. When the external environment impact on the system of FBM, the necessary and sufficient conditions for the optimization are offered through the stochastic maximum principle, Hamilton function and ItÔ formula in our work. To illustrate our study, we provide an example to demonstrate the obtained theoretical results, which is the expansion of certainty population system.